Conditional density function?

Hi, I'm not sure what the notation is supposed to mean in the highlighted box and how it relates to conditional probability:
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The definition of conditional probability that I'm familiar with is P(A|B) = P(A, B)/P(B). How (if at all) does that relate to what the authors have written there? Some special properties of the normal distribution perhaps?

Firstly, check that you understand how this relates to the previous line. It is simply making the subsititution

The notation appears to be a conditional pdf for Y, ie (very loosely*):

That is to say, in very loose terms* it is telling your the conditional probability of Y|X, if the parameter value is equal to theta. The parameter value has to be included because it made the substitution , which will be different for every possible value of

*in fact, pdfs do not give probabilities, but thats a seperate topic...

Last edited by SpringFan25; June 29th 2010 at 07:27 AM.
Reason: inaccuracies fixed